Republican Sens. Rob Portman, Pat Toomey and Rand Paul all introduced amendments that failed. But the legislation also attaches a provision aimed at forcing Senate Democrats to take up a budget for the first time in four years. If they do not, a "no budget, no pay" provision would withhold pay for members.

The debt-ceiling bill is that it is not technically a clean hike in the nation's debt limit. It's a suspension of the debt ceiling for a certain time period. On May 19, the debt limit will be raised by an amount "necessary to fund commitment incurred by the Federal Government that required payment." The Bipartisan Policy Center estimates that number will be around $450 billion.

If it passes and is signed into law quickly, it could delay the next potential debt-ceiling fight until August.

Now, the fiscal battles move on to sequestration — $1.2 trillion worth of cuts that will start kicking in on March 1.